The invention relates generally to medical imaging using X-ray computed tomography (CT), and more particularly the invention relates to reconstructing cone-beam x-ray scan data in tomographic imaging.
Computed tomography is an established medical technique for visualizing internal organs with high resolution. Both fan beams and cone beams (CB) of x-rays are employed in CT.
3D image reconstruction from circular CB data has been an active research field for the last two decades. While the exact reconstruction is achievable on the plane of the source trajectory (mid-plane) if the rotation angle is larger than π plus cone angle, it is impossible outside this central plane (off-plane). Many approximate algorithms have been developed for a circular CB scan. The filtered-backprojection (FBP-based reconstruction, due to Feldkamp et al. (FDK), is by far the most popular algorithm mainly for its structure of one-dimensional (1D) shift-invariant filtering. Although developed heuristically as an extension of the exact fan-beam reconstruction, this algorithm is very close to the optimal in the sense of without data extrapolation. It, however, results in severe CB artifacts in the case of short scan, which is very attractive in many applications, such as in the current C-arm CT. In order to handle the data redundancy, a simple but empirical modification of FDK uses Parker's weighting (P-FDK), which is accurate only for the mid-plane. Unlike the FDK algorithm on a full scan, this algorithm is not the optimal even in the sense of without data extrapolation. Nonetheless, the structure of 1D shift-invariant feature (for computation efficiency), other researchers apply a mathematically exact algorithm to the short scan source trajectory. The derived algorithm, however, does not necessarily achieve the optimal reconstruction.